What is Absolute Value?

In this lesson I’m going to explain what Absolute Value is, how to use it, and why we need it.

What is Absolute Value?

If you see some numbers in between two “bars” that look like this:

| -9 |

These bars | | are the Absolute Value sign.

What those bars are saying in “Math Talk” is:

“Take this number and take away it’s sign because all you need to think about here is how far away the number is from zero. Whether it’s negative or positive doesn’t matter right now. Right now all we need to focus on is how far away from zero this number is.”

So

| -9 | = | 9 |

Let’s look at an example together to make this more clear:

|-3| + 4 = ?

So in “Math Talk” this is saying, “Take the Absolute Value of -3 and add it to 4”.

Absolute Value means, “take away the sign from this number”.

So we get:

|3| + 4 = 7

Let’s look at another example, how about:

|5| + |12| = ?

Both those numbers are in between Absolute Value bars, but these numbers don’t have any signs, what do I do?

Nothing.

Remember, the Absolute Value sign is saying in “Math Talk”, “Look at these numbers and take away their signs (if they have any), because all I care about is how far away from zero they are on the number line.”

So we get |5| + |12| = 17

Let’s look at a number line to make this even more clear:

How do I use Absolute Value?

If you’re doing a math problem and you see some numbers inside the Absolute Value sign the first thing you do is treat them like they’re in parentheses. That means if there are any math problems in between the Absolute Value signs you do them first. (just like you would if they where in parentheses, because if you remember, when a math problem is inside parentheses, that means, “do me first.”)

Let’s look at an example:

|7 - 3| + 6 = ?

7 - 3 is in between the Absolute Value sign | |

So in “Math Talk” this is saying, “The first thing to do is just subtract 3 from 7.”

OK, let’s do that

7 - 3 = 4

So we get

|4| + 6 = ?

Now it’s saying, “Add the Absolute Value of 4 to the number 6.”

OK, let’s do that

|4| + 6 = 10

As you can see the answer is just a normal number. You don’t have to put the Absolute Value sign around the answer.

Why do I need to know about Absolute Value?

The Absolute Value sign is there to help you when the math problem your working on is more focused on the distance of things instead of the direction.

Absolute Value helps you answer questions related to , “How far?”

A real world example is my bank account:

If my bank account balance is $-5 and I have to pay my electric bill that’s $47, I need to know how much money to deposit into my bank account. I can figure it out easy by Adding together the Absolute Value of those 2 numbers:

|$-5| + $47 = ?

|$5| + $47 = $52

So I need to deposit at least $52 dollars into my bank account to cover the electric bill.

To Sum It All Up
If I point at a number and ask you, “What is the absolute value of that number?”
You would say, “The absolute value of that number is just that same number without any signs.”

Absolute Value is just how far away from zero the number is on the number line. It’s just that simple. Don’t try to over complicate it in your head.